Error

Try it out

Derivation

1. Split input into 3 regimes

2. if re < -8.215736410361959e+156

   1. Initial program 59.4

      \[\sqrt{re \cdot re + im \cdot im}\]

   2. Taylor expanded around -inf 7.2

      \[\leadsto \color{blue}{-1 \cdot re}\]

   3. Simplified7.2

      \[\leadsto \color{blue}{-re}\]

   if -8.215736410361959e+156 < re < 2.2296466947500767e+136

   1. Initial program 19.7

      \[\sqrt{re \cdot re + im \cdot im}\]

   if 2.2296466947500767e+136 < re

   1. Initial program 55.1

      \[\sqrt{re \cdot re + im \cdot im}\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt55.1

      \[\leadsto \sqrt{\color{blue}{\sqrt{re \cdot re + im \cdot im} \cdot \sqrt{re \cdot re + im \cdot im}}}\]

   4. Applied sqrt-prod55.1

      \[\leadsto \color{blue}{\sqrt{\sqrt{re \cdot re + im \cdot im}} \cdot \sqrt{\sqrt{re \cdot re + im \cdot im}}}\]

   5. Taylor expanded around inf 8.1

      \[\leadsto \color{blue}{re}\]
3. Recombined 3 regimes into one program.

4. Final simplification16.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;re \le -8.215736410361959 \cdot 10^{+156}:\\ \;\;\;\;-re\\ \mathbf{elif}\;re \le 2.2296466947500767 \cdot 10^{+136}:\\ \;\;\;\;\sqrt{im \cdot im + re \cdot re}\\ \mathbf{else}:\\ \;\;\;\;re\\ \end{array}\]

Reproduce

herbie shell --seed 2019021 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))

Details

Time bar (total: 4.8s)Debug log